Sectional curvature of projective invariant metrics on a strictly convex domain (Q675770)

In his paper [Tokyo J. Math. 8, 49-79 (1985; Zbl 0628.32027)] the first author had defined two metrics on convex domains in \(\mathbb{R}^n\) which are real analogs of well-known metrics on domains in \(\mathbb{C}^n\). For balls they coincide with the non-Euclidean metric of curvature \(-1\). Here it is shown that for both metrics the sectional curvatures tend to \(-1\) at the boundary.